This invention relates generally to a system which measures components of position or frequency as a function of time, and, more particularly to an In-Loop Integration Control System which is capable of producing consistent and accurate descriptions and predictions of any dynamic process, on line and in real time.
In the field of radar tracking, particularly, a problem has arisen, which, because of modern technology, is being thrust into the foreground. This problem relates the tracking of objects with such quality as to permit mount support or remote direction of very long focal length telescopes with sufficient accuracy and smoothness to allow successful high resolution photography and related tasks requiring similar performance.
Although high accuracy instrumentation exists today, such precise instrumentation does not possess sufficient accuracy in areas outside of "post-flight" determinations. That is, the instrumentation now available requires accurate data on-line. Upon a more detailed analysis of the prior art techniques, it has further become apparent that the limiting factor of prior instrumentation is not so much the equipment utilized but the data processing procedure which incorporates conventional "derivative" tracking technology.
For a better understanding of the "derivative tracking" technique let us review the development of the state vector approach. Trajectory may be described at any given instance or epoch by a single multielement vector which is a combination composed of time, position, velocity and acceleration (TPVA). This vector is known as a state vector. A series of state vectors are necessary for a description of a changing trajectory. Time must be the independent variable in any trajectory determination process because if timing errors exist, all other efforts may be negated. Investigation of trajectory measurement systems has shown that timing associated errors have been the largest single contributor to poor accuracy. Regardless how the trajectory is determined, some method of determining time-position derivatives must be employed, since the ordinary sensor can only measure position or its components. It is the accuracy of the derivative data which ultimately describes the accuracy of the trajectory. To assure accuracy, it is necessary that the effects of errors in any of the four vectorial components be observable so that the error growth may be controlled.
The most effective and commonly used trajectory determining method of the past employed a differentiation process. In this procedure an estimate of the derivatives are obtained from time-position measurements by first differences (differentiation) as shown: ##STR1##
Mathematically, instantaneous time-position derivatives can be obtained using the differentiation process and letting the time interval between samples approach zero. In practical measurements, however, discrete time measurement intervals occur, and the resulting time-position derivatives are averages which do not correspond exactly to any instantaneous value. As the overall time span is increased to derive the time-position derivatives, it becomes unlikely that the derivatives are correct for any particular time within the span. The derivatives obtained become averages over long periods, rather than representing actual values at any point along the trajectory. The situation is worse as measurements become noisier, since longer time intervals must be used and there is no guarantee that all noise (unwanted disturbances) will be filtered out. Another unfortunate aspect of the differentiation process is that all measured information (time and position) is used in computing time-position derivatives, so that no way of observing the result against other information is available. A decision can be made as to whether the time-position derivatives are "reasonable". There is no way results can be checked to determine whether noise was filtered out to leave good results, or whether noise remained and good data was filtered out to leave invalid results.
Perhaps another way to explain the problem is to point out that the conventional or derivative tracker is a device which seeks to keep a moving and perhaps maneuvering or accelerating target in the center of the field of view of the sensor (radar, telescope, etc.), by sensing errors, and transmitting these signals into the servo system in the mount to effect the corrections. The error signals are noisy. The process of following the target introduces lags into the data which are, in a practical sense, impossible to remove if the acceleration of the vehicle is unknown. The track is made rough because of the externally introduced unwanted disturbances (noise) which are amplified by the gain of the servo system. The center of the bore-sight is the reference for range, azimuth and elevation output data without regard to the position of the target in the field of view of the sensor or range gate.
An attempted solution to the problem was to filter the noisy boresight data prior to its introduction into the servo or, alternatively, to narrow the servo bandwidth. Either solution is undesirable because it results in an inability of the sensor to stay on track when the angular rates get high. Only a gross estimate of the state vector may be obtained using the time-position information sequence from the derivative or conventional system.